Yes the idea of a plastic or linoleum area for her when she is confined is a great one.
When I was 7 we got a puppy. I remember my mother covered a large area of the kitchen with linoleum and barricaded it off with a "fence" contraption my Dad made. The puppy's bed was in there, and water and food. And we could climb over. But the puppy had a good sized area to walk around in and play. Just if there were "accidents" it was so easy to mop up!
A big tarp is an excellent idea. They are not too expensive. And easy to replace if they get torn.
Any way to baby gate a kitchen area or other space with a vinyl or tile floor? Easier to clean than carpet......
Can you see a way to get either a dog walker or friend or family to drop in during the day for an hour or so? Not only is it a matter of peeing, it's a matter of a dog being confined for such a long period.
I know you can't help it. You have to work. But she needs to be outside sometimes during those 7 hours.
Probably she insists on going on the carpet because the smell from where she did it before still lingers. YOU might not be able to smell anything, but she will.
I still think some time out during the day, and a relief of the loneliness for her might help.
Good suggestions above, esp if you can contain her in a kitchen/service porch area? You might try putting some plastic on the floor and covering it with shredded paper. If you can collect an area that she goes on, try putting that in or on the paper so her scent will be there.
You can try getting an ex-pen or regular baby play yard thing (I don't know what they're called) and cover the floor under that with a plastic tarp maybe.